Abstract

We report ultra-compact surface-normal high-Q optical filters based on single- and double-layer stacked Fano resonance photonic crystal slabs on both Si and quartz substrates. A single layer photonic crystal filter was designed and a Q factor of 1,737 was obtained with 23 dB extinction ratio. With stacked double-layer photonic crystal configuration, the optical filter Q can increase to over 10,000,000 in design. Double-layer filters with quality factor of 9,734 and extinction ratio of 8 dB were experimentally demonstrated, for a filter design with target Q of 22,000.

]. With in-plane periodic modulation of dielectric constant in PhC slabs (PCS), the out-of-the-plane optical mode coupling is feasible with the Fano resonance effect, where the in-plane guided resonances above the lightline are strongly coupled to the out-of-the-plane radiation modes due to the phase matching provided by the periodic lattice structure. Therefore, these guided resonances can provide an efficient way to channel light from within the slab to the external environment, and vice versa. Such phenomenon was also investigated in one-dimensional grating structures, known as guided mode resonances (GMRs) [7

]. However, single layer PhC Fano filters offer limited quality factor Q and limited dispersion engineering capabilities for fine-tuning the output spectrum. It was reported that much higher Q Fano filters can be realized by multi-layer PhC coupling and lattice offset control [4

], we report here single- and double-layer Fano filters on silicon and on quartz substrates, with symmetric spectral lineshapes and much higher Q factors of 98,000-10,000,000 by design. We experimentally demonstrated double-layer filters with Q factors of 22,000 by design and ~10,000 by measurement. These high Q filters, can have extraordinary potentials in integrated photonics, optical communications, and sensing applications.

2. Device design

are the schematics of double-layer Fano resonance PhC optical filters on low index glass substrates, where key lattice parameters are defined as air hole radius (r), lattice period (a), thicknesses for top (t1), bottom (t2) Si PhC layers and the oxide buffer layer (tb) in between. Both single- and double-layer Fano resonance Si PhC filters were designed and optimized for high Q around 1,550 nm spectral band. The transmission spectrum and field plots were computed based on the Fourier Modal Method using a freely available Stanford Stratified Structure Solver (S4) software package [35

are key design parameters for a few optimized design structures, where S1-S3 are for single-layer and D1-D3 are for double-layer designs.

In an optimized single layer Fano filter design, Quality factor Q of 4,500 can be achieved with r/a ratio of 0.08, as shown in Table 1, S3. For the lattice constant a of 780 nm (Case S3), the corresponding air hole radius r is 62.4 nm. Though even higher Q is expected with further reduction in r/a ratio, achieving air holes with radius much smaller than 60 nm is challenging in fabrication. And potential degradation of air hole quality with radius smaller than 60 nm will lead to significant reduction in filter Q. Experimentally, we have demonstrated single layer filters based on PDMS transfer printing of single crystalline Si PhC nanomembranes on transparent low index glass substrate. A Q factor of 1,727 was obtained with 26 dB extinction ratio, for Design S1 with r/a = 0.08 and a = 765 nm.

On the other hand, much higher Q’s can be achieved by coupled double-layer Fano resonance PhC structures. Liu and Fan et al [4

] reported earlier that much higher Q can arise from the coupled dark states in the double-layer stacked PhC structures. We report here design and experimental demonstrations of coupled double-layer Fano resonance PhC filters. Some designs are summarized in Table 1, for cases D1 to D3. With the reduction in r/a value to 0.05, the filter Q increases to 98,000, which is one order of magnitude higher than the values in single-layer structures. Shown in Fig. 2

are the simulated transmission spectra for Designs S3 and D3, with Q of 4,500 and 98,000 respectively. Additionally, it was predicted that the double-layer PhC structure can excited extremely high Q mode (infinite in theory), by varying the coupling condition between two PhC layers [4

]. Based on the Design D2 parameters, transmission spectra were simulated by varying the buffer layer oxide thickness tb,.

For the double-layer structure, the simulated transmission spectra are plotted in Fig. 3(a)

Fig. 3 Simulation results for Design D2 with different buffer layer thicknesses tb: (a) Transmission spectra with different tb from 0 nm to 160 nm; (b) High Q resonant wavelengths and the corresponding Q values for different buffer thicknesses tb; (c) Zoom-in spectrum for the buffer thickness tb = 60 nm and filter Q of 10,000,000; and (d) Simulated E-field intensity profile at resonant wavelengths for three different tb values, where tb = 60 nm representing the highest Q condition for this design.

, with oxide buffer thicknesses range from 0 to 160 nm. With the increase of oxide buffer layer thicknesses, the high Q modes (shorter wavelength modes shown in Fig. 3(a) shift towards shorter wavelengths, with the filter Q value maximizes around 10,000,000 for buffer layer thickness tb = 60 nm, as shown in Fig. 3(b). Shown in Fig. 3(c) is the zoom-in spectral plot for the transmission dip with Q of 10,000,000. Simulated field distribution profiles for three cases close to the maximum Q are shown in Fig. 3(d), where strong field confinement is evident for the high Q transmission dips at optimal buffer layer thickness.

and 4(b) are scanning electron microscope (SEM) images of the fabricated single layer Fano filters on glass substrate. The single layer Fano filters were characterized with a tunable laser (1 pm tuning step) based setup for transmission measurement over wavelengths of 1490 nm to 1650 nm. The measured (blue solid line) and simulated (red dash line) transmission spectra are shown in Fig. 4(c), with zoom-ins shown in Fig. 4(d). Two transmission dips were found, at 1529.88 nm and 1564.62 nm. For the 1564.62 nm dip, the Q value of 1,737 was obtained, with 26 dB extinction ratio.

Two types of structures were prepared for double-layer PhC Fano filters on silicon and on quartz substrates, respectively. For the double-layer PhC Fano filters on SOI, low index oxide buffer layer was first formed by thermal oxidation of single-crystalline Si layer on the SOI substrate, followed by low pressure chemical vapor deposition (LPCVD) poly-Si deposition process, to form a poly-Si/thermal SiO2/crystalline-Si double-Si-layer structure.

A single EBL pattern was used to etch through the complete poly-Si/SiO2/c-Si structure, with a combination of two RIE steps for two Si layer etching and a short buffer oxide etch (BOE) dip for SiO2 buffer layer etching. For better etching selectivity, e-beam resist pattern was transferred onto a Cr metal layer to form a hard mask for the double-layer Si dry etching. Shown in Figs. 5(a)

Fig. 5 Cross-sectional SEM images for fabricated double-layer PhC Fano resonance filters based on Design D2 parameters: (a, b, c) Double-layer PhC structure was formed by poly-Si deposition on top of the SOI substrates; and (d) Double-layer PhC structure was formed by two steps of poly-Si deposition on quartz substrates. Notice the oxide buffer thicknesses are 20 nm, 160 nm, and 20 nm, for cases (b), (c), and (d), respectively.

The other double-layer PhC Fano filters on quartz substrates were formed by two steps of LPCVD poly-Si deposition process, with a plasma-enhanced chemical vapor deposited (PECVD) SiO2 layer sandwiched in between these two LPCVD poly-Si layers. The same E-beam patterning and etching processes were utilized for the 2D-PhC patterning. A SEM image is shown in Fig. 5(d).

The double-layer Fano filters were characterized by measuring transmission or reflection spectra for the two different configurations respectively. For the transmission measurement on a double-layer filter quartz substrate, a transmission dip at 1545.2 nm was obtained, with an estimated Q of 5,000 and 2.7dB extinction ratio (Fig. 6(a)

and 6(b)). For the reflection measurement on a double-layer filter on SOI substrate, a reflection peak was obtained at 1567 nm with Q factor of 9,734 and an 8dB extinction ratio (Fig. 6(c) and 6(d)). All these measured spectra match well with the simulated ones at these resonance locations (wit spectral dips or peaks). Measured Q values are less than the designed ones, which may come from the imperfect etching process of air holes, such as the conical shape and different hole sizes in this trilayer structure. We expect the filter performance can be improved with much higher Q factors by optimizing the fabrication process.

4. Conclusion

In conclusion, high Q surface-normal Fano resonance filters were designed and demonstrated experimentally based on single- and double-layer PhC structures. Higher Q filters can be obtained in double-layer PhC structures, with optimized Q of 22,000 by design and experimentally demonstrated Q close to 10,000. With fining tuning of double layer buffer layer thicknesses, it is possible to obtained extremely high Q (10,000,000 or higher) from the coupled dark state resonances [4

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